Large language models (LLMs) possess extensive world knowledge and have demonstrated strong potential for misinformation detection. A growing line of recent work prompts LLMs to produce structured reasoning before issuing a veracity judgment. However, we contend that such structured outputs do not spontaneously support the veracity decision. The emitted scores can satisfy the output schema while contributing little to veracity discrimination. Since annotating full reasoning paths is prohibitively costly for veracity tasks, we propose a Generation-Score Consistency framework that supervises through structured dimension scores and steers the LLM toward functional reasoning. Specifically, we train a compact score-to-label verifier on a small set of expert-annotated reasoning data, freeze it, and during supervised fine-tuning use a trainable score head to align the score-token hidden states of the LLM with the human-calibrated mapping. Introducing structured reasoning on its own costs accuracy relative to label-only supervision, while the consistency term recovers that cost and keeps the emitted scores coupled to the veracity decision. Controlled experiments on multimodal misinformation benchmarks show that the consistency term strengthens both veracity prediction and the discriminability of the emitted scores. Code and data are available at https://github.com/yun-nlp/Reasoning-Scores-for-Misinformation-Detection-EMNLP2026.